Search

We performed a series of 739 full numerical simulations of high energy collision of black holes to search for the maximum gravitational energy emitted $E_{rad}$, during their merger. We consider equal mass binaries with spins pointing along their orbital angular momentum $\vec{L}$ and perform a search over impact parameters $b$ and initial linear momenta $p/m=\gamma v$ to find the maximum $E_{rad}$ for a given spin $\vec{S}$. The total radiated energy proves to have a weak dependence on the intrinsic spin $s$ of the holes, for the sequence $s=+0.8, 0.0, -0.8$ studied here. We thus estimate the maximum $E_{rad}^{max}/M_{ADM}\approx25\%\pm2\%$ for these direct merger encounters. We also explore the radiated angular momentum and the maximum spin of the merger remnant (within these configurations), finding $\alpha_f^{max}=0.987$. We then use the zero frequency limit expansion to analytically model the radiated energy in the small impact parameter and large initial linear momentum regime., Comment: 11 pages, 7 figures, 4 tables

We perform a systematic study of eccentric orbiting nonspinning black hole binaries. We first make a technical study of the optimal full numerical techniques to apply to these studies. We choose different gauge parameters and Courant factors, $c=dx/dt$, and find an optimal value for it of 0.45. We also find the grid structure and global resolution that optimize accuracy and speed of current computational resources. With these choices we perform a study of the merger times $t_m$ as a function of eccentricity for configurations with comparable orbital energy content and find that they are well represented by the post-Newtonian factor $F(e)=(1+73e^2/24+37e^4/96)/(1-e^2)^{7/2}$ when merger times are normalized to their quasicircular values, i.e. $t_m(e)/t_m\approx F(e)$. We then perform a systematic coverage of five small-medium eccentricities up to $e\sim0.45$ and six mass ratios up to 8.5:1 producing a total of 30 simulations covering up to 25 orbits to merger to further model merger times and as a seed to a forthcoming new systematic catalog of gravitational waveforms from eccentric binary black holes to directly perform parameter estimations of gravitational waves events., Comment: 14 pages, 12 figures, 8 tables

We revisit the three black hole scenario with numerical relativity techniques to study hierarchical configurations where the inner binary contains highly spinning black holes. We find that the merger time of the binary gets a delay (with a number of orbits to merger increase), depending strongly with the distance to the orbiting third hole $D$ as $\sim1/D^{1.6\pm0.1}$. Notably, a different dependence from what we had found in the nonspinning case, $\sim1/D^{2.5}$. We interpret this effect as mostly due to a spin-orbit coupling between the third hole and the closest member of the binary in the successive approaches. This lead us next to study scattering configurations of the third hole with the binary in order to evaluate the extent of this ``sudden'' interactions, finding also a correlation of the delay in merger times with the closest distance, even for the nonspinning cases. We then explore the mass ratio dependence of the triple system by modeling binaries orbiting a larger black hole bearing masses ratios 8:1:1 and 18:1:1 in co-orbiting or counter-orbiting configurations, finding merger times increasing with increasing mass ratios and for the counter-orbiting cases., Comment: 12 pages, 13 figures, 8 tables. arXiv admin note: text overlap with arXiv:2308.07365

In the post-Newtonian (PN) expansion, we extend the determination of quasicircular orbital parameters to be used by subsequent full numerical simulations to the 3.5PN order, and find that this leads to lower eccentricities, $e$, than with our previous method that used up to 3PN order. We also supplement the computation of the radial infall due to radiation reaction and the location of the center of mass to 3.5PN order, providing explicit formulas. In addition, we consider the small mass ratio limit by explicitly including the Schwarzschild and Kerr limits, the later in quasi-isotropic as well as in our standard use of ADMTT coordinates. We evolve binaries with a $q=1/16$ mass ratio by using 3PN, 3.5PN, 3.5PN+Schwarzschild, 3.5PN+KerrQISO and 3.5PN+KerrADMTT quasicircular data for three different configurations where the larger hole intrinsic spins are $\chi^z=-0.8$, $-0.4$ and $+0.8$. Using different measures of eccentricity from the black hole trajectories and from the waveform amplitudes and phases, we determine a systematic reduction of eccentricities with respect to the 3PN initial values by factors of up to an order of magnitude, and reaching the desired $e\sim10^{-3}$ threshold., Comment: 13 pages, 4 figures, 3 tables

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome., Comment: 239 pages, 11 figures, white paper from the LISA Consortium Waveform Working Group, invited for submission to Living Reviews in Relativity, updated with comments from community

The Pulsar Monitoring in Argentina (PuMA) is a collaboration between the Argentine Institute for Radioastronomy (IAR) and the Rochester Institute of Technology (RIT) that since 2017 has been observing southern sky pulsars with high cadence using the two restored IAR antennas in the L-Band (1400MHz). We briefly review the first set of results of this program to study transient phenomena, such as magnetars and glitching pulsars, as well as to perform precise timing of millisecond pulsars. Access to lower frequency bands, where most of the pulsars are brighter, would allow us to reach additional pulsars, currently buried into the background noise. We identify two dozen additional glitching pulsars that could be observable in the 400MHz band by the IAR's projected Multipurpose Interferometer Array (MIA). We also discuss the relevance and challenges of single-pulse pulsar timing at low frequencies and the search for Fast Radio Burst (FRB) in the collected data since 2017 using machine learning techniques., Comment: 11 pages, 10 figures, 5 tables. arXiv admin note: text overlap with arXiv:2108.13462

We performed a series of 1381 full numerical simulations of high energy collision of black holes to search for the maximum recoil velocity after their merger. We consider equal mass binaries with opposite spins pointing along their orbital plane and perform a search of spin orientations, impact parameters, and initial linear momenta to find the maximum recoil for a given spin magnitude $s$. This spin sequence for $s=0.4, 0.7, 0.8, 0.85, 0.9$ is then extrapolated to the extreme case, $s=1$, to obtain an estimated maximum recoil velocity of $28,562\pm 342$ km/s, thus approximately bounded by $10\%$ the speed of light., Comment: 8 figures, 1 Table

We report here on the first results of a systematic monitoring of southern glitching pulsars at the Argentine Institute of Radioastronomy that started in the year 2019. We detected a major glitch in the Vela pulsar (PSR J0835$-$4510) and two small-glitches in PSR J1048$-$5832. For each glitch, we present the measurement of glitch parameters by fitting timing residuals. We then make an individual pulses study of Vela in observations before and after the glitch. We selected 6 days of observations around the major glitch on 2021 July 22 and study their statistical properties with machine learning techniques. We use Variational AutoEncoder (VAE) reconstruction of the pulses to separate them clearly from the noise. We perform a study with Self-Organizing Maps (SOM) clustering techniques to search for unusual behavior of the clusters during the days around the glitch not finding notable qualitative changes. We have also detected and confirm recent glitches in PSR J0742$-$2822 and PSR J1740$-$3015., Comment: 18 pages, 17 figures, 13 tables. To appear in MNRAS (2023)

We describe and study an instantaneous definition of eccentricity to be applied at the initial moment of full numerical simulations of binary black holes. The method consists of evaluating the eccentricity at the moment of maximum separation of the binary. We estimate it using up to third post-Newtonian (3PN) order, and compare these results with those of evolving (conservative) 3PN equations of motion for a full orbit and compute the eccentricity $e_r$ from the radial turning points, finding excellent agreement. We next include terms with spins up to 3.5PN, and then compare this method with the corresponding estimates of the eccentricity $e_r^{NR}$ during full numerical evolutions of spinning binary black holes, characterized invariantly by a fractional factor $0\leq f\leq1$ of the initial tangential momenta. It is found that our initial instantaneous definition is a very useful tool to predict and characterize even highly eccentric full numerical simulations., Comment: 7 pages, 7 figures, 1 Table

We explicitly demonstrate that current numerical relativity techniques are able to accurately evolve black hole binaries with mass ratios of the order of 1000:1. This proof of principle is relevant for future third generation (3G) gravitational wave detectors and space mission LISA, as by purely numerical methods we would be able to accurately compute gravitational waves from the last stages of black hole mergers, as directly predicted by general relativity. We perform a sequence of simulations in the intermediate to small mass ratio regime, $m_1^p/m_2^p = 1/7, 1/16, 1/32, 1/64, 1/128, 1/256, 1/512, 1/1024$, with the small hole starting from rest at a proper distance $D\approx13M$. We compare these headon full numerical evolutions with the corresponding semianalytic point particle perturbative results finding an impressive agreement for the total gravitational radiated energy and linear momentum as well as for the waveform spectra. We display numerical convergence of the results and identify the minimal numerical resolutions required to accurately solve for these very low amplitude gravitational waves. This work represents a first step towards the considerable challenge of applying numerical-relativity waveforms to interpreting gravitational-wave observations by LISA and next-generation ground-based gravitational-wave detectors., Comment: 7 pages, 5 figures, 2 tables

The Laser Interferometer Space Antenna (LISA) will be a transformative experiment for gravitational wave astronomy, and, as such, it will offer unique opportunities to address many key astrophysical questions in a completely novel way. The synergy with ground-based and space-born instruments in the electromagnetic domain, by enabling multi-messenger observations, will add further to the discovery potential of LISA. The next decade is crucial to prepare the astrophysical community for LISA's first observations. This review outlines the extensive landscape of astrophysical theory, numerical simulations, and astronomical observations that are instrumental for modeling and interpreting the upcoming LISA datastream. To this aim, the current knowledge in three main source classes for LISA is reviewed; ultracompact stellar-mass binaries, massive black hole binaries, and extreme or intermediate mass ratio inspirals. The relevant astrophysical processes and the established modeling techniques are summarized. Likewise, open issues and gaps in our understanding of these sources are highlighted, along with an indication of how LISA could help making progress in the different areas. New research avenues that LISA itself, or its joint exploitation with upcoming studies in the electromagnetic domain, will enable, are also illustrated. Improvements in modeling and analysis approaches, such as the combination of numerical simulations and modern data science techniques, are discussed. This review is intended to be a starting point for using LISA as a new discovery tool for understanding our Universe.

One of the open problems in developing binary black hole (BBH) waveforms for gravitational wave astronomy is to model the intermediate mass ratio regime and connect it to the extreme mass ratio regime. A natural approach is to employ the effective one body (EOB) approach to the two-body dynamics that, by design, can cover the entire mass ratio range and naturally incorporates the extreme mass ratio limit. Here we use recently obtained numerical relativity (NR) data with mass ratios $m_1/m_2=(7,15,\,32,\,64,\,128)$ to test the accuracy of the state-of-the-art EOB model TEOBResumS in the intermediate mass ratio regime. We generally find an excellent EOB/NR consistency around merger and ringdown for all mass ratios and for all available subdominant multipoles, except for the $\ell=m=5$ one. This mode can be crucially improved using the new large-mass ratio NR data of this paper. The EOB/NR inspirals are also consistent with the estimated NR uncertainties. We also use several NR datasets taken by different public catalogs to probe the universal behavior of the multipolar hierarchy of waveform amplitudes at merger, that smoothly connects the equal-mass BBH to the test-mass result. Interestingly, the universal behavior is strengthened if the nonoscillatory memory contribution is included in the NR waveform. Future NR simulations with improved accuracy will be necessary to further probe, and possibly quantitatively refine, the TEOBResumS transition from late inspiral to plunge in the intermediate mass ratio regime., Comment: 15 pages, 14 figures, submitted to Phys. Rev. D

This fourth release of the RIT public catalog of numerical relativity black-hole-binary waveforms \url{http://ccrg.rit.edu/~RITCatalog} consists of 1881 accurate simulations that include 446 precessing and 611 nonprecessing quasicircular/inspiraling binary systems with mass ratios $q=m_1/m_2$ in the range $1/128\leq q\leq1$ and individual spins up to $s/m^2=0.95$; and 824 in eccentric orbits in the range $0

We study individual pulses of Vela (PSR\ B0833-45\,/\,J0835-4510) from daily observations of over three hours (around 120,000 pulses per observation), performed simultaneously with the two radio telescopes at the Argentine Institute of Radioastronomy. We select 4 days of observations in January-March 2021 and study their statistical properties with machine learning techniques. We first use density based DBSCAN clustering techniques, associating pulses mainly by amplitudes, and find a correlation between higher amplitudes and earlier arrival times. We also find a weaker (polarization dependent) correlation with the mean width of the pulses. We identify clusters of the so-called mini-giant pulses, with $\sim10\times$ the average pulse amplitude. We then perform an independent study, with Self-Organizing Maps (SOM) clustering techniques. We use Variational AutoEncoder (VAE) reconstruction of the pulses to separate them clearly from the noise and select one of the days of observation to train VAE and apply it to thre rest of the observations. We use SOM to determine 4 clusters of pulses per day per radio telescope and conclude that our main results are robust and self-consistent. These results support models for emitting regions at different heights (separated each by roughly a hundred km) in the pulsar magnetosphere. We also model the pulses amplitude distribution with interstellar scintillation patterns at the inter-pulses time-scale finding a characterizing exponent $n_{\mathrm{ISS}}\sim7-10$. In the appendices we discuss independent checks of hardware systematics with the simultaneous use of the two radio telescopes in different one-polarization / two-polarizations configurations. We also provide a detailed analysis of the processes of radio-interferences cleaning and individual pulse folding., Comment: 19 pages

We revisit the definition of transverse frames and tetrad choices with regards to its application to numerically generated spacetimes, in particular those from the merger of binary black holes. We introduce the concept of local and approximate algebraic Petrov types in the strong field regime. We define an index $\mathcal{D}=\sqrt{12/I}\left(\Psi_2 - \Psi_3^2/\Psi_4\right)$ able to discriminate between Petrov types II and D and define regions of spacetime of those approximate types when used in conjunction with the speciality invariant $S=27J^2/I^3$. We provide an explicit example applying this method to Brill-Lindquist initial data corresponding to two nonspinning black holes from rest at a given initial separation. We find a doughnut-like region that is approximately of Petrov type II surrounded by an approximately Petrov type D region. We complete the study by proposing a totally symmetric tetrad fixing of the transverse frame that can be simply implemented in numerically generated spacetimes through the computation of spin coefficients ratios. We provide an application by explicitly deriving the Kerr-perturbative equations in this tetrad., Comment: 18 pages, 11 figures

We explore the benefits of adapted gauges to small mass ratio binary black hole evolutions in the moving puncture formulation. We find expressions that approximate the late time behavior of the lapse and shift, $(\alpha_0,\beta_0)$, and use them as initial values for their evolutions. We also use a position and black hole mass dependent damping term, $\eta[\vec{x}_1(t),\vec{x}_2(t),m_1,m_2]$, in the shift evolution, rather than a constant or conformal-factor dependent choice. We have found that this substantially reduces noise generation at the start of the numerical integration and keeps the numerical grid stable around both black holes, allowing for more accuracy with lower resolutions. We test our choices for this gauge in detail in a case study of a binary with a 7:1 mass ratio, and then use 15:1 and 32:1 binaries for a convergence study. Finally, we apply our new gauge to a 64:1 binary and a 128:1 binary to well cover the comparable and small mass ratio regimes., Comment: 22 pages, 21 figures, 8 tables

Using exclusively the 777 full numerical waveforms of the third Binary Black Holes RIT catalog, we reanalyze the ten black hole merger signals reported in LIGO/Virgo's O1/O2 observation runs. We obtain binary parameters, extrinsic parameters, and the remnant properties of these gravitational waves events which are consistent with, but not identical to previously presented results. We have also analyzed three additional events (GW170121, GW170304, GW170727) reported in Venumadhav et al. 2019, and found closely matching parameters. We finally assess the accuracy of our waveforms with convergence studies applied to O1/O2 events and found them adequate for current estimation of parameters., Comment: 16 pages, 8 figures, 7 tables

The third release of the RIT public catalog of numerical relativity black-hole-binary waveforms \url{http://ccrg.rit.edu/~RITCatalog} consists of 777 accurate simulations that include 300 precessing and 477 nonprecessing binary systems with mass ratios $q=m_1/m_2$ in the range $1/15\leq q\leq1$ and individual spins up to $s/m^2=0.95$. The catalog also provides initial parameters of the binary, trajectory information, peak radiation, and final remnant black hole properties. The waveforms are corrected for the center of mass drifting and are extrapolated to future null infinity. We successfully test this correction comparing with simulations of low radition content initial data. As an initial application of this waveform catalog we reanalyze all the peak radiation and remnant properties to find new, simple, correlations among them for practical astrophysical usage., Comment: 34 pages, 10 figures, 5 tables

We perform a sequence of binary black hole simulations with increasingly small mass ratios, reaching to a 128:1 binary that displays 13 orbits before merger. Based on a detailed convergence study of the $q=m_1/m_2=1/15$ nonspinning case, we apply additional mesh refinements levels around the smaller hole horizon to reach successively the $q=1/32$, $q=1/64$, and $q=1/128$ cases. Roughly a linear computational resources scaling with $1/q$ is observed on 8-nodes simulations. We compute the remnant properties of the merger: final mass, spin, and recoil velocity, finding precise consistency between horizon and radiation measures. We also compute the gravitational waveforms: its peak frequency, amplitude, and luminosity. We compare those values with predictions of the corresponding phenomenological formulas, reproducing the particle limit within 2%, and we then use the new results to improve their fitting coefficients., Comment: 6 pages, 4 figures

We explore different gauge choices in the moving puncture formulation in order to improve the accuracy of a linear momentum measure evaluated on the horizon of the remnant black hole produced by the merger of a binary. In particular, motivated by constant values studies, we design a gauge via a variable shift parameter $m\eta(\vec{r}(t))$ such that it takes a low asymptotic (and at the orbiting punctures) value, while about the standard value of 2 at the final hole horizon. This choice then follows the remnant black hole as it moves due to its net recoil velocity. We find that this choice keeps the accuracy of the binary evolution and, once the asymptotic value of the parameter $m\eta$ is chosen about or below 1.0, it produces more accurate results for the recoil velocity than the corresponding evaluation of the radiated linear momentum at infinity, for typical numerical resolutions. We also find that the choice of the $\partial_t$-gauge (at our working resolutions) is more accurate in this regard of computing recoil velocities than the $\partial_0$-gauge. Detailed studies of an unequal mass $q=m_1/m_2=1/3$ nonspinning binary are provided and then verified for other mass ratios $(q=1/2,1/5)$ and spinning $(q=1)$ binary black hole mergers., Comment: 14 pages, 9 figures

Binary black holes emit gravitational radiation with net linear momentum leading to a retreat of the final remnant black hole that can reach up to $\sim5,000$ km/s. Full numerical relativity simulations are the only tool to accurately compute these recoils since they are largely produced when the black hole horizons are about to merge and they are strongly dependent on their spin orientations at that moment. We present eight new numerical simulations of BBH in the hangup-kick configuration family, leading to the maximum recoil. Black holes are equal mass and near maximally spinning ($|\vec{S}_{1,2}|/m_{1,2}^2=0.97$). Depending on their phase at merger, this family leads to $\sim\pm4,700$ km/s and all intermediate values of the recoil along the orbital angular momentum of the binary system. We introduce a new invariant method to evaluate the recoil dependence on the merger phase via the waveform peak amplitude used as a reference phase angle and compare it with previous definitions. We also compute the mismatch between these hangup-kick waveforms to infer their observable differentiability by gravitational wave detectors, such as advanced LIGO, finding currently reachable signal-to-noise ratios, hence allowing for the identification of highly recoiling black holes having otherwise essentially the same binary parameters., Comment: 10 pages, 6 figures

We present a detailed investigation into the properties of GW170729, the gravitational wave with the most massive and distant source confirmed to date. We employ an extensive set of waveform models, including new improved models that incorporate the effect of higher-order waveform modes which are particularly important for massive systems. We find no indication of spin-precession, but the inclusion of higher-order modes in the models results in an improved estimate for the mass ratio of $(0.3-0.8)$ at the 90\% credible level. Our updated measurement excludes equal masses at that level. We also find that models with higher-order modes lead to the data being more consistent with a smaller effective spin, with the probability that the effective spin is greater than zero being reduced from $99\%$ to $94\%$. The 90\% credible interval for the effective spin parameter is now $(-0.01-0.50)$. Additionally, the recovered signal-to-noise ratio increases by $\sim0.3$ units compared to analyses without higher-order modes. We study the effect of common spin priors on the derived spin and mass measurements, and observe small shifts in the spins, while the masses remain unaffected. We argue that our conclusions are robust against systematic errors in the waveform models. We also compare the above waveform-based analysis which employs compact-binary waveform models to a more flexible wavelet- and chirplet-based analysis. We find consistency between the two, with overlaps of $\sim 0.9$, typical of what is expected from simulations of signals similar to GW170729, confirming that the data are well-described by the existing waveform models. Finally, we study the possibility that the primary component of GW170729 was the remnant of a past merger of two black holes and find this scenario to be indistinguishable from the standard formation scenario., Comment: 14 pages, 8 figures, final published version, samples available at https://git.ligo.org/katerina.chatziioannou/gw170729hm_datarelease

The RIT numerical relativity group is releasing the second public catalog of black-hole-binary waveforms \url{http://ccrg.rit.edu/~RITCatalog}. This release consists of 320 accurate simulations that include 46 precessing and 274 nonprecessing binary systems with mass ratios $q=m_1/m_2$ in the range $1/6\leq q\leq1$ and individual spins up to $s/m^2=0.95$. The new catalog contains search and ordering tools for the waveforms based on initial parameters of the binary, trajectory information, peak radiation, and final remnant black hole properties. The final black hole remnant properties provided here can be used to model the merger of black-hole binaries from its initial configurations. The waveforms are extrapolated to infinite observer location and can be used to independently interpret gravitational wave signals from laser interferometric detectors. As an application of this waveform catalog we reanalyze the signal of GW150914 implementing parameter estimation techniques that make use of only numerical waveforms without any reference to information from phenomenological models., Comment: 23 pages, 10 figures. Major extension of the GW150914 analysis

We explore spinning, precessing, unequal mass binary black holes to display the long term orbital angular momentum, $\vec{L}$, flip dynamics. We study two prototypical cases of binaries with mass ratios $q=1/7$ and $q=1/15$ and a misaligned spin of the large black hole (with an intrinsic spin magnitude of $S_2/m_2^2=0.85$). We conduct full numerical simulations, for nearly 14 and 18 orbits respectively, to evolve the binary down to merger and display a full $L$-flip cycle. The pattern of radiation of such systems is particularly interesting, displaying strong polarization-dependent variation of amplitudes at precessional frequencies, leading to distinctive observational consequences for ground, space, and pulsar timing based gravitational wave detectors. These waveform features are strongly directional dependent and measurements of gravitational waves polarizations can be exploited to disentangle the binary's parameters in various astrophysical scenarios., Comment: 9 pages, 11 figures, 4 tables. To appear in Physical Review D

We present the results of 74 new simulations of nonprecessing spinning black hole binaries with mass ratios $q=m_1/m_2$ in the range $1/7\leq q\leq1$ and individual spins covering the parameter space $-0.95\leq\alpha_{1,2}\leq0.95$ with one runs with spins of $\pm0.95$. We supplement those runs with 107 previous simulations to study the hangup effect in black hole mergers, i.e. the delay or prompt merger of spinning holes with respect to non spinning binaries. We perform the numerical evolution for typically the last ten orbits before the merger and down to the formation of the final remnant black hole. This allows us to study the hangup effect for unequal mass binaries leading us to identify the spin variable that controls the number of orbits before merger as $\vec{S}_{hu}\cdot{\hat{L}},$ where $\vec{S}_{hu}=(1+\frac12\frac{m_2}{m_1})\vec{S}_1+(1+\frac12\frac{m_1}{m_2})\vec{S}_2$. We also combine the total results of those 181 simulations to obtain improved fitting formulae for the remnant final black hole mass, spin and recoil velocity as well as for the peak luminosity and peak frequency of the gravitational strain, and find new correlations among them. This accurate new set of simulations enhances the number of available numerical relativity waveforms available for parameter estimation of gravitational wave observations., Comment: 26 pages, 13 figures

We evolve a binary black hole system bearing a mass ratio of $q=m_1/m_2=2/3$ and individual spins of $S^z_1/m_1^2=0.95$ and $S^z_2/m_2^2=-0.95$ in a configuration where the large black hole has its spin antialigned with the orbital angular momentum, $L^z$, and the small black hole has its spin aligned with $L^z$. This configuration was chosen to measure the maximum recoil of the remnant black hole for nonprecessing binaries. We find that the remnant black hole recoils at 500km/s, the largest recorded value from numerical simulations for aligned spin configurations. The remnant mass, spin, and gravitational waveform peak luminosity and frequency also provide a valuable point in parameter space for source modeling., Comment: 8 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1706.01980

We demonstrate that numerical relativity codes based on the moving punctures formalism are capable of evolving nearly maximally spinning black hole binaries. We compare a new evolution of an equal-mass, aligned-spin binary with dimensionless spin chi=0.99 using puncture-based data with recent simulations of the SXS Collaboration. We find that the overlap of our new waveform with the published results of the SXS Collaboration is larger than 0.999. To generate our new waveform, we use the recently introduced HiSpID puncture data, the CCZ4 evolution system, and a modified lapse condition that helps keep the horizon radii reasonably large., Comment: Version accepted to PRD. 7 pages, 8 figures

We present and assess a Bayesian method to interpret gravitational wave signals from binary black holes. Our method directly compares gravitational wave data to numerical relativity simulations. This procedure bypasses approximations used in semi-analytical models for compact binary coalescence. In this work, we use only the full posterior parameter distribution for generic nonprecessing binaries, drawing inferences away from the set of NR simulations used, via interpolation of a single scalar quantity (the marginalized log-likelihood, $\ln {\cal L}$) evaluated by comparing data to nonprecessing binary black hole simulations. We also compare the data to generic simulations, and discuss the effectiveness of this procedure for generic sources. We specifically assess the impact of higher order modes, repeating our interpretation with both $l\le2$ as well as $l\le3$ harmonic modes. Using the $l\le3$ higher modes, we gain more information from the signal and can better constrain the parameters of the gravitational wave signal. We assess and quantify several sources of systematic error that our procedure could introduce, including simulation resolution and duration; most are negligible. We show through examples that our method can recover the parameters for equal mass, zero spin; GW150914-like; and unequal mass, precessing spin sources. Our study of this new parameter estimation method demonstrates we can quantify and understand the systematic and statistical error. This method allows us to use higher order modes from numerical relativity simulations to better constrain the black hole binary parameters., Comment: 30 pages, 22 figures; submitted to PRD

We present the results of 14 simulations of nonspinning black hole binaries with mass ratios $q=m_1/m_2$ in the range $1/100\leq q\leq1$. For each of these simulations we perform three runs at increasing resolution to assess the finite difference errors and to extrapolate the results to infinite resolution. For $q\geq 1/6$, we follow the evolution of the binary typically for the last ten orbits prior to merger. By fitting the results of these simulations, we accurately model the peak luminosity, peak waveform frequency and amplitude, and the recoil of the remnant hole for unequal mass nonspinning binaries. We verify the accuracy of these new models and compare them to previously existing empirical formulas. These new fits provide a basis for a hierarchical approach to produce more accurate remnant formulas in the generic precessing case. They also provide input to gravitational waveform modeling., Comment: 8 pages, 4 figures

Recent detailed observations of the radio-loud quasar 3C 186 indicate the possibility that a supermassive recoiling black hole is moving away from the host galaxy at a speed of nearly 2100km/s. If this is the case, we can model the mass ratio and spins of the progenitor binary black hole using the results of numerical relativity simulations. We find that the black holes in the progenitor must have comparable masses with a mass ratio $q=m_1/m_2>1/4$ and the spin of the primary black hole must be $\alpha_2=S_2/m_2^2>0.4$. The final remnant of the merger is bounded by $\alpha_f>0.45$ and at least $4\%$ of the total mass of the binary system is radiated into gravitational waves. We consider four different pre-merger scenarios that further narrow those values. Assuming, for instance, a cold accretion driven merger model, we find that the binary had comparable masses with $q=0.70^{+0.29}_{-0.21}$ and the normalized spins of the larger and smaller black holes were $\alpha_2=0.94^{+0.06}_{-0.22}$ and $\alpha_1=0.95^{+0.05}_{-0.09}$. We can also estimate the final recoiling black hole spin $\alpha_f=0.93^{+0.02}_{-0.03}$ and that the system radiated $9.6^{+0.8}_{-1.4}\%$ of its total mass, making the merger of those black holes the most energetic event ever observed., Comment: 4 pages, 2 figures

The RIT numerical relativity group is releasing a public catalog of black-hole-binary waveforms. The initial release of the catalog consists of 126 recent simulations that include precessing and non precessing systems with mass ratios $q=m_1/m_2$ in the range $1/6\leq q\leq1$. The catalog contains information about the initial data of the simulation, the waveforms extrapolated to infinity, as well as information about the peak luminosity and final remnant black hole properties. These waveforms can be used to independently interpret gravitational wave signals from laser interferometric detectors and, Comment: 5 pages, 3 figures

We use post-Newtonian (PN) approximations to determine the initial orbital and spin parameters of black hole binaries that lead to low-eccentricity inspirals when evolved with numerical relativity techniques. In particular, we seek initial configurations that lead to very small eccentricities at small separations, as is expected for astrophysical systems. We consider three cases: (i) quasicircular orbits with no radial velocity, (ii) quasicircular orbits with an initial radial velocity determined by radiation reaction, and (iii) parameters obtained form evolution of the PN equations of motion from much larger separations. We study seven cases of spinning, nonprecessing, unequal mass binaries. We then use several definitions of the eccentricity, based on orbital separations and waveform phase and amplitude, and find that using the complete 3PN Hamiltonian for quasicircular orbits to obtain the tangential orbital momentum, and using the highest-known-order radiation reaction expressions to obtain the radial momentum, leads to the lowest eccentricity. The accuracy of this method even exceeds that of inspiral data based on 3PN and 4PN evolutions., Comment: 14 pages, 4 figures

We present the results of 61 new simulations of nonprecessing spinning black hole binaries with mass ratios $q=m_1/m_2$ in the range $1/3\leq q\leq1$ and individual spins covering the parameter space $-0.85\leq\alpha_{1,2}\leq0.85$. We additionally perform 10 new simulations of nonspinning black hole binaries with mass ratios covering the range $1/6\leq q<1$. We follow the evolution for typically the last ten orbits before merger down to the formation of the final remnant black hole. This allows for assessment of the accuracy of our previous empirical formulae for relating the binary parameters to the remnant final black hole mass, spin and recoil. We use the new simulation to improve the fit to the above remnant formulae and add a formula for the peak luminosity of gravitational waves, produced around the merger of the two horizons into one. We find excellent agreement (typical errors $\sim0.1-0.2\%$) for the mass and spin, and within $\sim5\%$ for the recoil and peak luminosity. These formulae have direct application to parameter estimation techniques applied to LIGO observations of gravitational waves from binary black hole mergers., Comment: 22 pages, 11 figures

In fall of 2015, the two LIGO detectors measured the gravitational wave signal GW150914, which originated from a pair of merging black holes. In the final 0.2 seconds (about 8 gravitational-wave cycles) before the amplitude reached its maximum, the observed signal swept up in amplitude and frequency, from 35 Hz to 150 Hz. The theoretical gravitational-wave signal for merging black holes, as predicted by general relativity, can be computed only by full numerical relativity, because analytic approximations fail near the time of merger. Moreover, the nearly-equal masses, moderate spins, and small number of orbits of GW150914 are especially straightforward and efficient to simulate with modern numerical-relativity codes. In this paper, we report the modeling of GW150914 with numerical-relativity simulations, using black-hole masses and spins consistent with those inferred from LIGO's measurement. In particular, we employ two independent numerical-relativity codes that use completely different analytical and numerical methods to model the same merging black holes and to compute the emitted gravitational waveform; we find excellent agreement between the waveforms produced by the two independent codes. These results demonstrate the validity, impact, and potential of current and future studies using rapid-response, targeted numerical-relativity simulations for better understanding gravitational-wave observations., Comment: 11 pages, 3 figures, submitted to Classical and Quantum Gravity

We give a unified description of the flip-flop effect in spinning binary black holes and the anti-alignment instability in terms of real and imaginary flip-flop frequencies. We find that this instability is only effective for mass ratios $0.5

We use fully nonlinear numerical relativity techniques to study high energy head-on collision of nonspinning, equal-mass black holes to estimate the maximum gravitational radiation emitted by these systems. Our simulations include improvements in the construction of initial data, subsequent full numerical evolutions, and the computation of waveforms at infinity. The new initial data significantly reduces the spurious radiation content, allowing for initial speeds much closer to the speed of light, i.e. $v\sim0.99c$. Using these new techniques, We estimate the maximum radiated energy from head-on collisions to be $E_{\text{max}}/M_{\text{ADM}}=0.13\pm0.01$. This value differs from the second-order perturbative $(0.164)$ and zero-frequency-limit $(0.17)$ analytic computations, but is close to those obtained by thermodynamic arguments $(0.134)$ and by previous numerical estimates $(0.14\pm0.03)$., Comment: 11 pages, 10 figures

We study the spin dynamics of individual black holes in a binary system. In particular we focus on the polar precession of spins and the possibility of a complete flip of spins with respect to the orbital plane. We perform a full numerical simulation that displays these characteristics. We evolve equal mass binary spinning black holes for $t=20,000M$ from an initial proper separation of $d=25M$ down to merger after 48.5 orbits. We compute the gravitational radiation from this system and compare it to 3.5 post-Newtonian generated waveforms finding close agreement. We then further use 3.5 post-Newtonian evolutions to show the extension of this spin {flip-flop} phenomenon to unequal mass binaries. We also provide analytic expressions to approximate the maximum {flip-flop} angle and frequency in terms of the binary spins and mass ratio parameters at a given orbital radius. Finally we discuss the effect this spin {flip-flop} would have on accreting matter and other potential observational effects., Comment: Largely updated paper with 19 pages and 22 figures

We revisit the modeling of the properties of the remnant black hole resulting the merger of a black-hole binary as a function of the parameters of the binary. We provide a set of empirical formulas for the final mass, spin and recoil velocity of the final black hole as a function of the mass ratio and individual spins of the progenitor. In order to determine the fitting coefficients for these formulas, we perform a set of 128 new numerical evolutions of precessing, unequal-mass black-hole binaries, and fit to the resulting remnant mass, spin, and recoil. In order to reduce the complexity of the analysis, we chose configurations that have one of the black holes spinning, with dimensionless spin alpha=0.8, at different angles with respect to the orbital angular momentum, and the other non-spinning. In addition to evolving families of binaries with different spin-inclination angles, we also evolved binaries with mass ratios as small as q=1/6. We use the resulting empirical formulas to predict the probabilities of black hole mergers leading to a given recoil velocity, total radiated gravitational energy, and final black hole spin., Comment: New version includes correction for errors in the published version (see Erratum Phys. Rev. D 94, 029901 (2016))

We solve the Hamiltonian and momentum constraints of general relativity for two black holes with nearly extremal spins and relativistic boosts in the puncture formalism. We use a non-conformally-flat ansatz with an attenuated superposition of two Lorentz-boosted, conformally Kerr or conformally Schwarzschild 3-metrics and their corresponding extrinsic curvatures. We compare evolutions of these data with the standard Bowen-York conformally flat ansatz (technically limited to intrinsic spins $\chi=S/M^2_{\text{ADM}}=0.928$ and boosts $P/M_{\text{ADM}}=0.897$), finding, typically, an order of magnitude smaller burst of spurious radiation and agreement with inspiral and merger. As a first case study, we evolve two equal-mass black holes from rest with an initial separation of $d=12M$ and spins $\chi_i=S_i/m_i^2=0.99$, compute the waveforms produced by the collision, the energy and angular momentum radiated, and the recoil of the final remnant black hole. We find that the black-hole trajectories curve at close separations, leading to the radiation of angular momentum. We also study orbiting nonspinning and moderate-spin black-hole binaries and compare these with standard Bowen-York data. We find a substantial reduction in the nonphysical initial burst of radiation which leads to cleaner waveforms. Finally, we study the case of orbiting binary black-hole systems with spin magnitude $\chi_i=0.95$ in an aligned configuration and compare waveform and final remnant results with those of the SXS Collaboration, finding excellent agreement. This represents the first moving punctures evolution of orbiting and spinning black holes exceeding the Bowen-York limit. Finally, we study different choices of the initial lapse and lapse evolution equation in the moving punctures approach to improve the accuracy and efficiency of the simulations., Comment: 23 pages, 32 figures. Version accepted to PRD

We study binary spinning black holes to display the long term individual spin dynamics. We perform a full numerical simulation starting at an initial proper separation of $d\approx25M$ between equal mass holes and evolve them down to merger for nearly 48 orbits, 3 precession cycles, and half of a flip-flop cycle. The simulation lasts for $t=20000M$ and displays a total change in the orientation of the spin of one of the black holes from initially aligned with the orbital angular momentum to a complete anti-alignment after half of a flip-flop cycle. We compare this evolution with an integration of the 3.5 Post-Newtonian equations of motion and spin evolution to show that this process continuously flip-flops the spin during the lifetime of the binary until merger. We also provide lower order analytic expressions for the maximum flip-flop angle and frequency. We discuss the effects this dynamics may have on spin growth in accreting binaries and on the observational consequences for galactic and supermassive binary black holes., Comment: 5 pages, 5 figures. To appear in Physical Review Letters

We perform a set of 36 nonprecessing black-hole binary simulations with spins either aligned or counteraligned with the orbital angular momentum in order to model the final mass, spin, and recoil of the merged black hole as a function of the individual black hole spin magnitudes and the mass ratio of the progenitors. We find that the maximum recoil for these configurations is $V_{max}=526\pm23\,km/s$, which occurs when the progenitor spins are maximal, the mass ratio is $q_{max}=m_1/m_2=0.623\pm0.038$, the smaller black-hole spin is aligned with the orbital angular momentum, and the larger black-hole spin is counteraligned ($\alpha_1=-\alpha_2=1$). This maximum recoil is about $80\,km/s$ larger than previous estimates, but most importantly, because the maximum occurs for smaller mass ratios, the probability for a merging binary to recoil faster than $400\,km/s$ can be as large as $17\%$, while the probability for recoils faster than $250\, km/s$ can be as large as $45\%$. We provide explicit phenomenological formulas for the final mass, spin, and recoil as a function of the individual BH spins and the mass difference between the two black holes. Here we include terms up through fourth-order in the initial spins and mass difference, and find excellent agreement (within a few percent) with independent results available in the literature. The maximum radiated energy is $E_{\rm rad}/m\approx11.3\%$ and final spin $\alpha_{\rm rem}^{\rm max}\approx0.952$ for equal mass, aligned maximally spinning binaries., Comment: 19 pages, 25 figures, revtex 4

We perform a set of 38 numerical simulations of equal-mass BH binaries in a configuration where the BH spins in the binary are equal in both magnitude and direction, to study precession effects. We vary the initial direction of the total spin S with respect to the orbital angular momentum L, covering the 2 dimensional space of orientation angles with 38 configurations consisting of 36 configurations distributed in the azimuthal angle phi and polar angle theta, and two configurations on the poles. In all cases, we set the initial dimensionless BH spins to 0.8. We observe that during the late-inspiral stage, the total angular momentum of the system J remains within 5 deg of its original direction, with the largest changes in direction occurring when the spins are nearly counter-aligned with the orbital angular momentum. We also observe that the angle between S and L is nearly conserved during the inspiral phase. These two dynamical properties allow us to propose a new phenomenological formula for the final mass and spin of merged BHs in terms of the individual masses and spins of the progenitor binary at far separations. We determine coefficients of this formula (in the equal-mass limit) using a least-squares fit to the results of this new set of 38 runs, an additional set of five new configurations with spins aligned/counteraligned with the orbital angular momentum, and over 100 recent simulations. We find that our formulas reproduce the remnant mass and spin of these simulations to within a relative error of 2.5%. We discuss the region of validity of this dynamical picture for precessing unequal-mass binaries. Finally, we perform a statistical study to see the consequence of this new formula for distributions of spin-magnitudes and remnant masses with applications to BH-spin distributions and gravitational radiation in cosmological scenarios involving several mergers., Comment: Text and figures improved for clarity

We evolve a set of 32 equal-mass black-hole binaries with collinear spins (with intrinsic spin magnitudes $|\vec{S}_{1,2}/m^2_{1,2}|=0.8$) to study the effects of precession in the highly nonlinear plunge and merger regimes. We compare the direction of the instantaneous radiated angular momentum, $\hat{\delta J}_{\rm rad}(t)$, to the directions of the total angular momentum, $\hat{J}(t)$, and the orbital angular momentum, $\hat{L}(t)$. We find that $\hat{\delta J}_{\rm rad}(t)$ approximately follows $\hat{L}$ throughout the evolution. During the orbital evolution and merger, we observe that the angle between $\vec{L}$ and total spin $\vec{S}$ is approximately conserved to within $1^\circ$, which allows us to propose and test models for the merger remnant's mass and spin. For instance, we verify that the \hangup effect is the dominant effect and largely explains the observed total energy and angular momentum radiated by these precessing systems. We also verify that the total angular momentum, which significantly decreases in magnitude during the inspiral, varies in direction by less than $\sim 5^\circ$. The maximum variation in the direction of $\vec J$ occurs when the spins are nearly antialigned with the orbital angular momentum. Based on our results, we conjecture that transitional precession, which would lead to large variations in the direction of $\vec J$, is not possible for similar-mass binaries and would require a mass ratio $m_1/m_2\lesssim1/4$., Comment: Updated to published version

The Numerical-Relativity-Analytical-Relativity (NRAR) collaboration is a joint effort between members of the numerical relativity, analytical relativity and gravitational-wave data analysis communities. The goal of the NRAR collaboration is to produce numerical-relativity simulations of compact binaries and use them to develop accurate analytical templates for the LIGO/Virgo Collaboration to use in detecting gravitational-wave signals and extracting astrophysical information from them. We describe the results of the first stage of the NRAR project, which focused on producing an initial set of numerical waveforms from binary black holes with moderate mass ratios and spins, as well as one non-spinning binary configuration which has a mass ratio of 10. All of the numerical waveforms are analysed in a uniform and consistent manner, with numerical errors evaluated using an analysis code created by members of the NRAR collaboration. We compare previously-calibrated, non-precessing analytical waveforms, notably the effective-one-body (EOB) and phenomenological template families, to the newly-produced numerical waveforms. We find that when the binary's total mass is ~100-200 solar masses, current EOB and phenomenological models of spinning, non-precessing binary waveforms have overlaps above 99% (for advanced LIGO) with all of the non-precessing-binary numerical waveforms with mass ratios <= 4, when maximizing over binary parameters. This implies that the loss of event rate due to modelling error is below 3%. Moreover, the non-spinning EOB waveforms previously calibrated to five non-spinning waveforms with mass ratio smaller than 6 have overlaps above 99.7% with the numerical waveform with a mass ratio of 10, without even maximizing on the binary parameters., Comment: 51 pages, 10 figures; published version

We perform several black-hole binary evolutions using fully nonlinear numerical relativity techniques at separations large enough that low-order post-Newtonian expansions are expected to be accurate. As a case study, we evolve an equal-mass nonspinning black-hole binary from a quasicircular orbit at an initial coordinate separation of D=100M for three different resolutions. We find that the orbital period of this binary (in the numerical coordinates) is T=6422M. The orbital motion agrees with post-Newtonian predictions to within 1%. Interestingly, we find that the time derivative of the coordinate separation is dominated by a purely gauge effect leading to an apparent contraction and expansion of the orbit at twice the orbital frequency. Based on these results, we improved our evolution techniques and studied a set of black hole binaries in quasi-circular orbits starting at D=20M, D=50M, and D=100M for ~ 5, 3, and 2 orbits, respectively. We find good agreement between the numerical results and post-Newtonian predictions for the orbital frequency and radial decay rate, radiated energy and angular momentum, and waveform amplitude and phases. The results are relevant for the future computation of long-term waveforms to assist in the detection and analysis of gravitational waves by the next generation of detectors as well as the long-term simulations of black-hole binaries required to accurately model astrophysically realistic circumbinary accretion disks., Comment: Revised version with longer and waveforms, new plots showing omega versus proper distance, a list of orbital periods and eccentricity, and a dozen new references

We present results from an extensive study of 88 precessing, equal-mass black-hole binaries with large spins (83 with intrinsic spins of 0.8 and 5 with intrinsic spins of 0.9)and use these data to model new nonlinear contributions to the gravitational recoil imparted to the merged black hole. We find a new effect, the cross kick, that enhances the recoil for partially aligned binaries beyond the hangup kick effect. This has the consequence of increasing the probabilities of recoils larger than 2000 km/s by nearly a factor two, and, consequently, of black holes getting ejected from galaxies, as well as the observation of large differential redshifts/blueshifts in the cores of recently merged galaxies., Comment: Fix sign error in table 1. Repeated terms dropped in table 5

We study the convergence properties of our implementation of the 'moving punctures' approach at very high resolutions for an equal-mass, non-spinning, black-hole binary. We find convergence of the Hamiltonian constraint on the horizons and the L2 norm of the Hamiltonian constraint in the bulk for sixth and eighth-order finite difference implementations. The momentum constraint is more sensitive, and its L2 norm shows clear convergence for a system with consistent sixth-order finite differencing, while the momentum and BSSN constraints on the horizons show convergence for both sixth and eighth-order systems. We analyze the gravitational waveform error from the late-inspiral, merger, and ringdown. We find that using several lower-order techniques for increasing the speed of numerical relativity simulations actually lead to apparently non-convergent errors. Even when using standard high-accuracy techniques, rather than seeing clean convergence, where the waveform phase is a monotonic function of grid resolution, we find that the phase tends to oscillate with resolution, possibly due to stochastic errors induced by grid refinement boundaries. Our results seem to indicate that one can obtain gravitational waveform phases to within 0.05 rad. (and possibly as small as 0.015 rad.), while the amplitude error can be reduced to 0.1%. We then compare with the waveforms obtained using the cZ4 formalism. We find that the cZ4 waveforms have larger truncation errors for a given resolution, but the Richardson extrapolation phase of the cZ4 and BSSN waveforms agree to within 0.01 rad., even during the ringdown., Comment: version accepted to PRD

We study conformally-flat initial data for an arbitrary number of spinning black holes with exact analytic solutions to the momentum constraints constructed from a linear combination of the classical Bowen-York and conformal Kerr extrinsic curvatures. The solution leading to the largest intrinsic spin, relative to the ADM mass of the spacetime epsilon_S=S/M^2_{ADM}, is a superposition with relative weights of Lambda=0.783 for conformal Kerr and (1-Lambda)=0.217 for Bowen-York. In addition, we measure the spin relative to the initial horizon mass M_{H_0}, and find that the quantity chi=S/M_{H_0}^2 reaches a maximum of \chi^{max}=0.9856 for Lambda=0.753. After equilibration, the final black-hole spin should lie in the interval 0.9324

The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search and parameter-estimation algorithms using numerically generated waveforms, and to foster closer collaboration between the numerical relativity and data analysis communities. The first NINJA project used only a small number of injections of short numerical-relativity waveforms, which limited its ability to draw quantitative conclusions. The goal of the NINJA-2 project is to overcome these limitations with long post-Newtonian - numerical relativity hybrid waveforms, large numbers of injections, and the use of real detector data. We report on the submission requirements for the NINJA-2 project and the construction of the waveform catalog. Eight numerical relativity groups have contributed 63 hybrid waveforms consisting of a numerical portion modelling the late inspiral, merger, and ringdown stitched to a post-Newtonian portion modelling the early inspiral. We summarize the techniques used by each group in constructing their submissions. We also report on the procedures used to validate these submissions, including examination in the time and frequency domains and comparisons of waveforms from different groups against each other. These procedures have so far considered only the $(\ell,m)=(2,2)$ mode. Based on these studies we judge that the hybrid waveforms are suitable for NINJA-2 studies. We note some of the plans for these investigations., Comment: Presented at Amaldi 9

Physics in curved spacetime describes a multitude of phenomena, ranging from astrophysics to high energy physics. The last few years have witnessed further progress on several fronts, including the accurate numerical evolution of the gravitational field equations, which now allows highly nonlinear phenomena to be tamed. Numerical relativity simulations, originally developed to understand strong field astrophysical processes, could prove extremely useful to understand high-energy physics processes like trans-Planckian scattering and gauge-gravity dualities. We present a concise and comprehensive overview of the state-of-the-art and important open problems in the field(s), along with guidelines for the next years. This writeup is a summary of the "NR/HEP Workshop" held in Madeira, Portugal from August 31st to September 3rd 2011., Comment: 68 pages, 4 Figures